Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

A new Lyapunov design method for nonlinear process control

Due to the character of the original source materials and the nature of batch digitization, quality control issues may be present in this document. Please report any quality issues you encounter to [email protected], referencing the URI of the item.Includes bibliographical references (leaves 42-47).Issued also on microfiche from Lange Micrographics.The present research work proposes a new nonlinear controller synthesis approach that is based on the methodological principles of Lyapunov design. In particular, it introduces a notion of short-horizon model-based prediction and optimization of the rate of ``energy dissipation'' of the system, as it is realized through the derivative of an appropriately selected control Lyapunov function. The latter is computed by solving Zubov's partial differential equation based on the system's drift vector field. A nonlinear state feedback control law with two adjustable parameters is derived as the solution of an optimization problem, that is formulated on the basis of the aforementioned control Lyapunov function and closed-loop performance characteristics. A set of key properties of the proposed control law is examined. Key properties include continuity, unity static (steady-state) gain in closed-loop, closed-loop internal stability and enlargement of the quadratic closed-loop stability region estimates. The proposed Laypunov design method is evaluated in a representative chemical reactor example which exhibits nonminimum-phase behaviour, and the main design aspects are illustrated through simulation studies

Discrete-Time Kalman Filter Design for Linear Infinite-Dimensional Systems

As the optimal linear filter and estimator, the Kalman filter has been extensively utilized for state estimation and prediction in the realm of lumped parameter systems. However, the dynamics of complex industrial systems often vary in both spatial and temporal domains, which take the forms of partial differential equations (PDEs) and/or delay equations. State estimation for these systems is quite challenging due to the mathematical complexity. This work addresses discrete-time Kalman filter design and realization for linear distributed parameter systems. In particular, the structural- and energy-preserving Crank–Nicolson framework is applied for model time discretization without spatial approximation or model order reduction. In order to ensure the time instance consistency in Kalman filter design, a new discrete model configuration is derived. To verify the feasibility of the proposed design, two widely-used PDEs models are considered, i.e., a pipeline hydraulic model and a 1D boundary damped wave equation

Trajectory determination for pipelines using an inspection robot and pipeline features

Geographic trajectory of a pipeline is important information for pipeline maintenance and leak detection. Although accurate trajectory of a ground pipeline usually can be directly measured by using global positioning system technology, it is much difficult to determine trajectory for an underground pipeline where global positioning system signal cannot be received. In this paper, a new method to determine trajectory for an underground pipeline by using a pipeline inspection robot is proposed. The robot is equipped with a low-cost inertial measurement unit and odometers. The kinematic model, measurement model and error propagation model are established for estimating position, velocity and attitude of the robot. The path reconstruction algorithm for the robot is proposed to improve accuracy of trajectory determination based on pipeline features. The experiment is given to illustrate that the position errors of the proposed method are less than 40% of that of the standard extended Kalman filter

Model predictive control for regular linear systems

The present work extends known finite-dimensional constrained optimal control realizations to the realm of well-posed regular linear infinite-dimensional systems modeled by partial differential equations. The structure-preserving Cayley–Tustin transformation is utilized to approximate the continuous-time system by a discrete-time model representation without using any spatial discretization or model reduction. The discrete-time model is utilized in the design of model predictive controller accounting for optimality, stabilization, and input and output/state constraints in an explicit way. The proposed model predictive controller is dual-mode in the sense that predictive controller steers the state to a set where exponentially stabilizing unconstrained feedback can be utilized without violating the constraints. The construction of the model predictive controller leads to a finite-dimensional constrained quadratic optimization problem easily solvable by standard numerical methods. Two representative examples of partial differential equations are considered.submittedVersionPeer reviewe

Linear Model Predictive Control for Schrödinger Equation

The paper considers the finite-horizon constrained optimal control problem for Schrödinger equation with boundary controls and boundary observations. The plant is mapped from continuous to discrete time using the Cayley-Tustin transform, which preserves input-output-stability of the plant. The proposed transformation is structure and energy preserving and does not induce order reduction associated with the spatial discretization. The controller design setting leads to the finite horizon constrained quadratic regulator problem, which is easily realized and accounts in explicit manner for input and output/state constraints. The model predictive control (MPC) design is realized for Schrödinger equation and the results are illustrated with numerical simulations showing successful stabilization of Schrödinger equation with simultaneous satisfaction of input and output/state constraints.acceptedVersionPeer reviewe

Adaptive Fault Estimation for Hyperbolic PDEs

The new adaptive fault estimation scheme is proposed for a class of hyperbolic partial differential equations in this paper. The multiplicative actuator and sensor faults are considered. There are two cases that require special consideration: (1). only one type of fault (actuator or sensor) occurs; (2). two types of faults occurred simultaneously. To solve the problem of fault estimation, three challenges need to be solved: (1). No prior information of fault type is known; (2). Unknown faults are always coupled with state and input; (3). Only one boundary measurement is available. The original plant is converted to Observer canonical form. Two filters are proposed and novel adaptive laws are developed to estimate unknown fault parameters. With the help of the proposed update laws, the true state of the faulty plant can be estimated by the proposed observers composed of two filters. By selecting a suitable Lyapunov function, it is proved that under unknown external disturbance, the estimation errors of state parameters and fault parameters decay to arbitrarily small value. Finally, the validity of the proposed observer and adaptive laws is verified by numerical simulation